Suppose that X is a random variable for which the p.d.f. or the p.f. is f (x|), where the value of the parameter is

Suppose that X is a random variable for which the p.d.f. or the p.f. is f (x|θ), where the value of the parameter θ is unknown but must lie in an open interval Ω. Let I0(θ) denote the Fisher information in X. Suppose now that the parameter θ is replaced by a new parameter μ, where θ = ψ(μ), and ψ is a differentiable function. Let I1(μ) denote the Fisher information in X when the parameter is regarded as μ. Show that I1(μ) = [ψ'(μ)]2I0[ψ(μ)].